On the dependency of division on multiplication: selective loss for conceptual knowledge of multiplication

This study reports the case of a patient (AG) whose main calculation problem was with multiplication that was severely affected at all levels including that of conceptual knowledge. In contrast AG's problems with addition, subtraction and division were much less conspicuous and just involved the use of procedures. For all these latter operations, and for division in particular, conceptual knowledge was spared. Despite his procedural problems, AG in fact was fully aware that division consists of finding out how many times a given quantity is contained in another quantity. Thus while he was able to reach the correct results for division by subtracting the divisor from the dividend, he never used the reverse strategy to complete multiplication operations, i.e. add the number for as many times as the multiplier to complete the operation, and showed no awareness that this was what multiplying means, even when explicit suggestions were made by the examiner. The existence of AG's case could not be expected on the basis of theories holding that division depends on multiplication and that is not separately represented in semantic memory. It follows, therefore, that the extent to which division depends on multiplication needs to be reconsidered.